International Journal of Automotive Technology, Vol. 15, No. 2, pp. 237−252 (2014) DOI 10.1007/s12239−014−0025−7

Copyright © 2014 KSAE/ 076−07 pISSN 1229−9138/ eISSN 1976−3832

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS J. HA1) and H. HUH2)* 1)

Metal Forming Research Group, Songdo Product Application Center, POSCO Global R&D Center, 180-1 Songdo-dong, Yeonsu-gu, Incheon 406-840, Korea 2) School of Mechanical, Aerospace & Systems Engineering, KAIST, Daejeon 305-701, Korea (Received 1 November 2013; Revised 12 December 2013; Accepted 3 January 2014)

ABSTRACT−This paper proposes a dynamic failure criterion for laser welds to describe the strain-rate dependent failure behavior of laser welds in the crash analysis of an auto-body. The failure criterion has been developed from experiments with nine different conditions of combined normal and shear loading including the normal loading and the pure shear loading. The experiments were carried out with a high speed material testing machine at intermediate strain rates ranging from quasi-static to 100 s-1. The dynamic failure tests were examined with four cases of the 25 mm stitch-type laser weld of CR340 1.2t, the 20 mm stitch-type laser weld of CR340 1.2t, the 25 mm stitch-type laser weld of SPCC 1.0t and the O-type laser weld with the 8 mm diameter of CR340 1.2t in order to evaluate the influence of the strain rate on the failure loads with respect to the base metal and the bead geometry. Based on the experimental data, a novel failure criterion was proposed for the description of the failure behavior of laser welds on the basis of the quasi-static failure criterion. The failure criteria are divided into two regions: the base metal failure criterion is expressed as a β-norm function; and the interfacial failure criterion is expressed as an exponential function. For the both failure criteria, the strain-rate sensitivity of the normal and the shear failure load are assigned as an exponential function of the logarithm of the strain rate. The change of the shear failure load with the increase of the strain rate is also considered to accurately construct the failure criteria. The failure mode and the onset of failure of the laser welds are determined when the maximum value reaches unity. The dynamic failure criterion proposed provides a fairly accurate description of the failure load obtained from the experiments under dynamic combined loading conditions. KEY WORDS : Laser welding, Dynamic failure load, Combined normal and shear load, Intermediate strain rate, Dynamic failure criterion

1. INTRODUCTION

condition. The failure behavior of laser welds under an impact condition, however, can differ substantially from that under a statically loading condition. Therefore, the implications of the quasi-static behavior of laser welds in crash analysis leads to inaccurate numerical results of the deformation behavior and the energy absorption of an autobody component. The failure researches of laser welds have recently gained the focus of extensive experimental and theoretical studies to evaluate the durability and the crashworthiness of an auto-body. It is important to estimate the strength of laser welds when an impact load is applied to the structure to understand the failure characteristics. A failure criterion is proposed from these estimations to provide an appropriate failure criterion for laser welds used in the structural analyses or crashworthiness assessment of autobody members. For these purposes, lap-shear tests and cross-tension tests have been performed to estimate the failure loads of laser-welded regions (Kuppuswamy et al., 2007; Kavamura and Batalha, 2008; Lee et al., 2011; Kang et al., 2012; Ha and Huh, 2013). Kuppuswamy et al. (2007) carried out various types of failure tests such as lap-shear

The laser welding process is in the limelight of the autobody assembly industry as an alternative process of spot welding to improve productivity and crash-worthiness with reduced costs. It is, therefore, important to understand the failure characteristics of laser welds of an auto-body member when a large load is applied to evaluate the crashworthiness of the structure. The failure of laser welds is likely to be observed prior to the failure of a base metal when a large load is applied to the auto-body structure because extremely high stress is concentrated around a bead. The quasi-static failure of laser welds has been the challenging subject of extensive experimental and theoretical studies recently (Kuppuswamy et al., 2007; Kavamura and Batalha, 2008; Lee et al., 2011; Kang et al., 2012; Ha and Huh, 2013). These studies assumed that the failure of laser welds was independent of the strain rate in the early stage of design and the failure tests of the laser welds were carried out under the quasi-static loading *Corresponding author. e-mail: [email protected] 237

238

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tests, tensile/shear tests and coach-peel tests to apply various loading angles to laser welds under quasi-static loading conditions. Based on an empirical consideration of material and sheet thickness combinations, a substitute finite element model was developed for modeling Cshaped laser welds for crash simulations. Kavamura and Batalha (2008) estimated the mechanical strength of spot welds and laser welds using experimental and numerical methods under combined loading conditions using the Arcan jig. Lee et al. (2011) carried out failure tests using lap-shear specimens under quasi-static loading conditions and performed two-dimensional plane strain finite element analyses to understand the failure mode of laser welds in lap-shear specimens. Based on these investigations, they proposed a failure or separation methodology of laser welds in lap-shear specimens using finite element analyses by adopting the Gurson yield function. Kang et al. (2012) examined the laser weldability for hot-press-forming steels with and without Al-Si coating. The butt and lap joint welding characteristics of hot-press-forming steels were investigated, and trials were carried out to improve the weld strength in lap joint welding. Ha and Huh (2013) proposed a new failure criterion for the various types of laser welds under combined normal and shear loading conditions based on experimental results. The failure criterion proposed by these researchers is divided into two regions of a base metal failure and an interfacial failure to describe the failure mode change accurately. However, this criterion did not consider the influence of the strain rate on the failure load of laser welds. These researches are, however, not enough to understand the failure characteristics and to provide the failure criterion of laser welds compared with a spot weld because laser welds in automotive components are subjected to complicated dynamic loading conditions when they undergo crashed deformation. Several researches have studied the effect of the strain rate on the strength of a spot weld (Lin et al., 2004; Sun and Khaleel, 2007; Song et al., 2008; Song and Huh, 2011; Wood et al., 2009; Wood et al., 2010; Chao et al., 2010; Wang et al., 2010; Yang et al., 2010; Langrand and Markiewicz, 2010) to investigate the failure characteristics and criterion of spot welds under dynamic combined loading conditions. Lin et al. (2004) conducted dynamic failure tests of a spot weld in mild steel under normal and combined normal/shear loading conditions using a gas-driven impact machine. Sun and Khaleel (2007) employed servo-hydraulic testing machines to conduct dynamic failure tests of spot welds. Song et al. (2008) also conducted dynamic failure tests of spot welds in SPRC340R using a high speed material test machine and lap-shear specimens. They introduced a dynamic failure model of a spot weld to describe the strain-rate dependent failure contours under combined normal and shear loading conditions based on their failure model, which was developed for quasi-static loading conditions. Their failure model proposed employed the β-norm shaped function to

describe the quasi-static failure loads of spot welds (Song and Huh, 2011). Wood et al. (2009, 2010) described a strain rate dependent spot weld failure model with both experiments and numerical simulations. Chao et al. (2010) and Wang et al. (2010) suggested a dynamic failure model, which was expressed as a function of the loading rate using dynamic failure tests of spot welds using a drop tester. Yang et al. (2010) proposed a simplified finite element model of spot welds with a strain rate effect. Langrand and Markiewicz (2010) carried out extensive experiments of the failure strength of spot welds under static and dynamic combined loading. While there are both an effective testing methodology and available data to model the dynamic failure behavior of spot welds, an appropriate failure criterion of laser welds under the impact loading condition has not been reported yet. The purpose of this paper is to propose a dynamic failure criterion for laser welds to describe the strain-rate dependent failure behavior of laser welds under dynamic combined normal and shear loading conditions. The failure criterion has been suggested based on the experimental results from nine different conditions of combined normal and shear loading including the normal loading and the pure shear loading. Dynamic failure tests of the laser welds were carried out with a high speed material testing machine operated by a servo-hydraulic system (Huh et al., 2012). Using specially designed testing fixtures and jigs for specimens, nine different combined loads with a constant ratio of the shear load to the normal load were imposed on the laser welds during the tests (Ha and Huh, 2013). In order to evaluate the influence of the strain rate on the failure loads with respect to the base metal and the bead geometry, the dynamic failure tests were examined with four kinds of laser welding cases at intermediate strain rates of 1/sec, 10/sec and 100/sec because the strain rate of

Figure 1. High speed material testing machine.

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 239

the crushed auto-body lies in that intermediate strain rate range. The strain-rate sensitivity of the failure loads were evaluated by plotting the normal failure loads and the pureshear failure loads in a logarithmic scale of the strain rate. Based on the experimental data, a novel failure criterion was proposed to describe the failure behavior of the laser welds on the basis of the quasi-static failure criterion. The dynamic failure criterion proposed provides a fairly accurate description of the failure load obtained from experiments under dynamic combined loading conditions.

2. DYNAMIC FAILURE TESTS OF A SPOT WELD UNDER COMBINED LOADING CONDITIONS 2.1. High Speed Material Testing Machine The dynamic response of laser welds at intermediate strain rates has to be obtained using a proper experimental apparatus. Lin et al. (2004) studied the dynamic failure

loads of spot welds using a horizontal gas-driven impact machine. Bayraktar et al. (2004) used a Charpy impact tester and Zhang et al. (2001) adopted an impact tester that used pendulums. Chao et al. (2010), Wang et al. (2010) and Yang et al. (2010) suggested a dynamic failure model of spot welds using a drop tester. These experimental apparatuses could not apply the constant loading speed to weldment. In order to perform the dynamic failure tests of weldment under a constant loading speed, servo-hydraulic testing machines have been typically employed in most recent studies (Sun and Khaleel, 2007; Song et al., 2008; Wood et al., 2009; Wood et al., 2010). In the present experiment, the servo-hydraulic high speed material testing machine (Huh et al., 2012) shown in Figure 1 was utilized in order to obtain the dynamic failure loads of laser welds at intermediate strain rates. The machine has a maximum stroke velocity of 7800 mm/sec, a maximum load of 30 kN and a maximum displacement of 300 mm. For a dynamic failure test, the instrument that measures the load and the displacement should have good response in the dynamic motion since failure tests at intermediate strain rates last only for several milli-seconds. The machine equipment is set up with a piezo-electric load cell of Kistler 9051A. The displacement is acquired by a linear displacement transducer (LDT) from the Sentech company. During the operation of the highspeed material testing machine, a function generator transmits an input signal to the servo controller to control the displacement via a feedback system by comparing the measured displacement with the input signal. 2.2. Testing Fixtures and Specimens In order to impose a combined normal and shear load and a pure-shear load on laser welds, specially designed testing fixtures and specimens were adopted in this research (Ha and Huh, 2013). The testing system for the combined loading conditions shown in Figure 2 contains the pinjoints that eliminate the horizontal force and the bending moment. The testing fixture for the pure-shear loading condition prevents the rotation of the bead during failure tests. The specimens for the combined loading conditions shown in Figure 3 involve guide plates that prevent the unfavorable rotation of the bead due to bending deformation. The specimen for the pure-shear loading conditions shown in Figure 4 is designed with a dog-bone shape to concentrate the plastic deformation around the laser weld. The testing fixture and specimen ensure a combined loading condition with a constant ratio of the shear load to the normal load during the test. Therefore, as explained in Figure 5, the applied load FZ can be decomposed into the normal load FN and the shear load FS at the bead region using the simple trigonometric functions:

Figure 2. Dynamic failure tests using the high speed material testing machine: (a) mounting of a testing set; (b) testing fixtures at various loading angles.

FN = FZ cos θ

(1)

FS = FZ sin θ

(2)

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Figure 3. Cross tension test specimens used in the failure tests at loading angles of 0o, 15o, 30o, 45o, 60o, 75o, 80o and 85o: (a) stitch-type laser weld; (b) O-type laser welds.

where FN, FS and θ denote the normal load, the shear load and the initial inclined angle with respect to the pulling direction, respectively. The inclined angle θ is equal to the loading angle, which represents the angle between the loading direction and the centerline of the specimen. Laser welds of steel plate commercially cold-rolled (SPCC) and cold-rolled (CR) steel sheet with the ultimate tensile strength of about 340 MPa and a thickness of 1.2 mm (CR340) is selected for failure tests since SPCC 1.0t and CR340 1.2t are widely used in the auto-body. SPCC is a mild steel grade steel sheet and CR340 is HSS grad steel sheet. The engineering stress−strain curves of each steel sheet at various strain rates are shown in Figure 6. The chemical compositions and the quasi-static material properties are also summarized in Table 1 and Table 2, respectively. Dynamic failure tests for the 25 mm stitchtype laser welds of CR340 1.2t and SPCC 1.0t, the 20 mm stitch-type laser welds of CR340 1.2t and the 8 mm diameter O-type laser welds of CR340 1.2t were examined in this paper. Prior to the laser welding of a specimen, the specimen surface was wiped with a weak acetone solution using a cloth to remove grease and dirt from its surface. The laser welding was then performed using a 6 kW-class fiber and disk laser with a remote welding system, and the welding parameters used in this paper are shown in Table 3.

Figure 4. Pure-shear test specimens used in the failure tests at the loading angle of 90o: (a) stitch-type laser weld; (b) Otype laser welds.

Figure 5. Decomposition of the applied loads on a laser weld into a normal and a shear component at a loading angle of θ : (a) stitch-type laser welds; (b) O-type laser welds.

Figure 6. Engineering stress−strain curves at various strain rates: (a) SPCC 1.0t; (b) CR340 1.2t.

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 241

Table 1. Chemical composition of the steel sheets tested. Chemical composition [wt%]

Material

C

Si

Mn

P

S

SPCC 1.0t

0.0025 0.034

0.120

0.018

0.015

CR340 1.2t

0.041

0.500

0.035

0.025

0.030

Table 2. Quasi-static material properties of the steel sheets tested. Yield strength Tensile strength Elongation [MPa] [MPa] [%]

Material

Figure 7. Finite element model of a specimen for simulation of dynamic failure tests of a laser weld: (a) stitch-type laser weld; (b) O-type laser weld.

The laser welding conditions were set as a full penetration condition. Dynamic failure tests of the laser welds were conducted at nine different loading angles with the testing fixtures shown in Figure 2. The specimen used in the tests at loading angles of 0o, 15o, 30o, 45o, 60o, 75o, 80o and 85o is shown in Figure 3. Additionally, a pure-shear test was performed using the specimen shown in Figure 4 in order to obtain the failure load at a loading angle of 90o. 2.3. Dynamic Failure Test Conditions In the crashworthiness assessment of an auto-body, strain rates up to 200 s-1 are commonly observed. This is within the range of the intermediate strain rate, and the strength of

SPCC 1.0t

157.3

291.7

49.8

CR340 1.2t

242.1

348.4

37.5

a laser weld should be evaluated at this range. The crosshead speeds in the dynamic failure tests were determined by finite element analysis in order to conduct failure tests for a laser-welded region with the designated strain rate. Finite element analyses of dynamic failure tests were first performed with different loading speeds. The averaged strain rates were then calculated at the end elements of a bead for the stitch-type laser welds and the circumferential elements of the interface between the base metal and the heat-affected zone (HAZ) for the O-type laser welds because the failure of a laser weld was initiated in these regions with respect to the laser welding shape. The finite element models of the specimens were discretized as shown in Figure 7. The material used for the specimen was a high strength steel of CR340 with a thickness of 1.2 mm. The flow stress of the steel sheets is shown in Figure 6 (b), and the value was obtained from the tensile tests performed following the experimental procedure reported by Huh et al. (2012). The material properties of the laser-welded bead and the HAZ were estimated using the experimental results originally found by Ha et al. (2008). The commercial explicit code ABAQUS/ Explicit was utilized in the numerical simulation. The averaged strain rates of the laser weld failure initiating regions are shown in Figure 8 with different tensile speeds. The figure shows that the specimen deforms with constant strain rates and that the averaged strain rates

Table 3. Laser welding conditions for the steel sheets tested. Material

Laser source

Laser power [kW]

Welding speed [m/min]

SPCC 1.0t 25 mm stitch

Disk laser (TRUMPF)

3.40

4.50

450

600

on the base metal surface

CR340 1.2t 25 mm stitch

Fiber laser (IPG Photonics)

4.00

3.00

450

500

on the base metal surface

Disk laser (TRUMPF)

4.00

5.00

450

600

on the base metal surface

CR340 1.2t 20 mm stitchand φ 8 mm circle

Focal length Beam diameter [mm] [µm]

Focus

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Table 4. Experimental conditions for the failure tests of a laser-welded region. Type

Testing machine

Strain rate [s-1]

Crosshead speed [m/sec]

Loading angle [o]

Quasi-static

INSTRON 5583

0.004

5 × 10-3

1

0.0125

10

0.125

100

1.25

0o 15o 30o 45o 60o 75o 80o 85o 90o

Dynamic

High Speed Material Testing Machine (HSMTM)

Figure 8. Numerical results for the dynamic failure tests of a laser-welded region at the loading angle of 0o: (a) CR340 1.2t 25 mm stitch; (b) CR340 1.2t 20 mm stitch; (c) CR340 1.2t φ 8 mm circle.

Figure 9. Load−displacement curves of the CR340 1.2t 25 mm stitch laser welds for various loading angles at the strain rate of : (a) 1 s-1; (b) 10 s-1; (c) 100 s-1.

of the elements are 1 s-1, 10 s-1 and 100 s-1 at tensile speeds of 0.0125 m/sec, 0.125 m/sec and 1.25 m/sec, respectively. Based on the numerical results, the testing conditions for the dynamic failure tests of the laser welds are summarized

in Table 4. The testing fixtures were mounted in the high speed material testing machine as shown in Figure 2 (b). Dynamic failure tests at strain rates of 1 s-1, 10 s-1 and 100 s-1 were conducted under nine different loading conditions until

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 243

Table 5. Dynamic failure loads of the CR340 1.2t 25 mm stitch laser weld at various loading angles. Quasi-static Loading angle [o]

Dynamic

-1

-1

0.004 s

o

10 s-1

1s

100 s-1

1st

2nd

3rd

1st

2nd

3rd

1st

2nd

3rd

1st

2nd

3rd

11.32

12.33

12.53

12.86

13.00

13.27

13.27

13.79

14.26

13.80

14.25

14.30

o

10.51

11.50

11.81

11.97

12.34

12.35

12.65

12.84

13.12

12.95

13.09

13.45

o

11.51

12.48

12.48

13.26

13.49

13.59

13.50

14.00

14.21

13.83

14.41

14.64

o

12.89

12.98

13.16

13.44

14.31

14.50

14.85

14.90

14.92

14.85

15.01

15.85

o

60

13.12

13.94

14.24

14.50

14.85

14.91

15.10

15.64

15.73

15.89

15.95

16.29

75o

14.45

14.53

14.87

14.91

15.76

15.81

16.24

16.30

16.45

16.47

16.72

17.01

o

14.45

14.19

13.99

14.81

14.83

15.58

15.83

15.89

15.91

16.16

16.09

16.59

o

14.04

13.77

13.10

14.68

14.44

14.36

15.06

15.39

15.64

15.41

15.48

15.97

o

10.69

10.83

11.02

11.56

12.01

12.22

12.34

12.73

12.75

12.77

12.82

12.88

0

15

30 45

80 85 90

Table 6. Dynamic failure loads of the CR340 1.2t 20 mm stitch laser weld at various loading angles. Loading angle [o] o

0

Quasi-static -1

0.004 s 1st

2nd

Dynamic -1

1s 1st

2nd

10 s-1 1st

2nd

100 s-1 1st

2nd

9.19 9.30 9.79 9.64 10.07 10.03 10.28 10.29

o

8.73 8.69 9.19 9.13 9.67 9.46 9.83 9.81

o

8.73 8.69 9.14 9.09 9.47 9.49 9.73 9.66

o

9.03 9.25 9.48 9.56 10.08 10.01 10.25 10.21

o

9.76 9.63 10.17 10.23 10.55 10.45 10.86 10.67

o

10.43 10.60 10.88 10.81 11.15 11.11 11.26 11.31

o

10.33 10.32 10.61 10.56 10.94 10.86 11.11 11.02

o

9.76 9.54 10.05 10.01 10.39 10.28 10.61 10.54

o

8.03 8.04 8.58 8.56 8.89 8.90 9.52 9.30

15 30 45 60 75

80 85 90

the laser weld failed and the specimen was separated into two components. The load and displacement were measured simultaneously during each test. The load was measured using the load cell in the testing machine and the displacement was calculated from the relative movement of the two pull bars. 2.4. Experimental Results Dynamic failure tests were carried out at nine different loading angles to evaluate the failure loads of the laserwelded specimen at the intermediate strain rate with the testing conditions described in Section 2.3. The failure tests were carried out at least twice for each loading case. The load−displacement curves for the 25 mm stitch-type laser welds of the CR340 1.2t specimens at various loading angles with strain rates of 1 s-1, 10 s-1 and 100 s-1 are shown

in Figure 9. A load ringing phenomenon was observed because of the inertia effect of a fixture during the dynamic failure tests at a strain rate of 100 s-1. In order to identity the failure load at a strain rate of 100 s-1, oscillating load− displacement curves were fitted with a form of the Lüdwik equation F = A + B(u – C)n from 0o to 30o. The failure loads were calculated assuming that the failure mode of 100 s-1 was similar to those of the quasi-statics as shown in Figure 10 (a). For loading angles from 45o to 85o, the load− displacement curves were fitted with an adjacent-averaging filter maintaining the shape of the critical load (Huh et al., 2012). The failure loads were also calculated assuming that the failure mode of 100 s-1 was similar to those of the quasistatic condition as shown in Figure 10 (c). The failure loads obtained from the tests for the 25 mm stitch-type laser welds of CR340 1.2t and SPCC 1.0t, the 20 mm stitch-type laser welds of CR340 1.2t and the 8 mm diameter O-type Table 7. Dynamic failure loads of the SPCC 1.0t 25 mm stitch laser weld at various loading angles. Loading angle [o] o

0

Quasi-static -1

0.004 s 1st

2nd

Dynamic -1

1s 1st

2nd

10 s-1 1st

2nd

100 s-1 1st

2nd

8.15 8.04 8.30 8.37 8.42 8.53 8.56 8.63

o

7.74 7.98 8.07 8.26 8.49 8.35 8.57 8.53

o

8.14 8.03 8.38 8.28 8.65 8.47 8.75 8.73

o

8.37 8.31 8.55 8.63 8.74 8.76 9.08 8.95

o

8.68 8.71 9.01 9.18 9.43 9.30 9.77 9.62

o

9.65 9.84 10.11 10.00 10.27 10.33 10.50 10.47

o

10.10 10.41 10.55 10.48 10.63 10.76 10.79 11.00

o

85

9.67 10.03 10.14 10.24 10.37 10.39 10.48 10.55

90o

7.89 7.54 7.97 8.07 8.23 8.28 8.31 8.32

15 30 45 60 75 80

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J. HA and H. HUH

Table 8. Dynamic failure loads of the CR340 1.2t φ 8 mm circle laser weld at various loading angles. Loading angle [o] o

0

o

Quasi-static -1

0.004 s 1st

2nd

10.25 10.05

Dynamic -1

1s

10 s-1

1st 2nd 1st -

2nd

100 s-1 1st

2nd

- 10.49 10.78 11.70 11.29

15

-

-

-

-

30o

9.09

9.06

-

-

9.51 9.88 10.16 10.59

-

-

-

-

45o

9.43

9.97 10.23 10.88 10.88

9.36

-

-

o

10.37 10.50

-

- 11.17 11.32 12.04 12.20

o

12.19 12.46

-

- 13.58 13.18 14.23 14.14

o

11.39 11.44

-

- 12.49 11.94 13.03 12.84

o

10.77 10.87

-

- 11.44 11.38 12.25 12.42

9.94

-

- 11.09 10.62 11.55 11.71

60

75 80 85

o

90

9.99

laser welds of CR340 1.2t at various loading angles and strain rates are listed in Table 5, 6, 7 and 8, respectively. The results of the quasi-static failure tests (Ha and Huh, 2013) were also listed here. The corresponding maximum loads were obtained from the tests for the 25 mm stitch-type laser welds of CR340 1.2t and SPCC 1.0t, the 20 mm stitch-type laser welds of CR340 1.2t and the 8 mm diameter O-type laser welds of CR340 1.2t as shown in Figure 11. The transition point is observed around a loading angle of 75o because of the change in the failure mode from base metal failure to interfacial failure for the 25 mm stitch-type laser welds of CR340 1.2t (Ha and Huh, 2013). In the case of the base metal failure, the corresponding maximum load decreases with an increase of the loading angle from 0o to 15o, whereas the maximum load increases as the loading angle increases in the range of 15o to 75o as shown in Figure 11 (a). In the case of interfacial failure, the corresponding maximum load decreases with an increase of the loading angle from 75o to 90o because the initial crack propagates in the shear load dominant direction and the bead is more brittle than the base metal after the laser welding processes. The transition point and the failure tendency are observed differently with respect to a base metal, a bead length and a bead shape as shown in Figure 11. When the strain rate changes from 0.004 s-1 to 100 s-1, the maximum loads for the laser-welded specimens increase with an increase of the strain rate. In order to examine the effect of the strain rate on the failure load of the laser welds, the normal and shear failure loads were plotted in a logarithmic scale of the strain rate as shown in Figure 12. The figure shows that the normal and shear failure load increases with an increase of the strain rate. Moreover, the strain-rate sensitivity of the normal and shear failure load can be interpolated in terms of the quasi-static failure load and the logarithm of the

Figure 10. Calculation of the failure load of a laser-welded region for CR340 1.2t at a strain rate of 100/sec: (a) 0o; (b) 45o. strain rate. Failure contours of the laser welds at different strain rates were also constructed by decomposing the failure loads measured in the experiment into two components along the normal and shear directions using Equations (1) and (2). These contours were plotted in the force domain as shown in Figure 13, which shows that the failure contour expands as the strain rate increases. In the case of the base metal failure, the shear failure load increases as the normal failure load decreases with an increase of the loading angle. The base metal failure contour shows a near-elliptical shape. Therefore, the failure of laser welds can be predicted by a failure criterion similar to that of spot welds (Song and Huh, 2011). The transition point is observed around a loading angle between 75o and 80o because of the change in the failure mode. In the case of the interfacial failure, the shear failure load decreases as the normal failure load decreases with an increase of the loading angle. Therefore, a new dynamic failure criterion has to be developed to predict the failure load and the change of the failure mode considering the strain-rate effect. A dynamic failure criterion is proposed to describe the strain-rate dependent failure contour of laser welds in the following section.

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 245

3. DYNAMIC FAILURE CRITERION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS The dynamic failure load of laser welds is quite different from the statically loaded case as shown in the experimental results. A failure behavior of laser welds with the quasi-static failure criterion proposed by Ha and Huh (2013) cannot predict the accurate failure load under a dynamic loading condition. In this paper, a dynamic failure criterion is newly proposed to describe the strain-rate dependent failure contour of laser welds under combined normal and shear loading conditions. The dynamic failure criterion is derived from the quasi-static failure criterion shown in Equation (3), max. ϕ( φ b( fn, fs ), φ i ( fn, fs ) ) = 1

(3a)

2

f f f f 2 φ b ( fn, fs ) = ⎛⎝ -----n-⎞⎠ + β ⎛⎝ -----n-⎞⎠ ⎛⎝ ----s-⎞⎠ + ⎛⎝ ----s-⎞⎠ FN F N FS FS fs φ i ( fn, fs ) = -----------F*s ( fn ) F*S ( fn) = K ( a + fn )n

(3b) (3c) (3d)

where Equation (3b) is the failure criterion for the base metal failure region and Equation (3c) is the failure criterion for the interfacial failure region. The maximum value of the failure criteria is obtained after calculating the failure criteria of Equation (3b) and Equation (3c) with the normal load and the shear load acting on the laser welds.

The failure mode and the failure of the laser welds are determined when the maximum value reaches unity in Equation (3a). It was already verified that the criterion is appropriate to describe the quasi-static failure loads of the laser welds for various steel sheets under the combined loading conditions (Ha and Huh, 2013). In the dynamic loading cases, the failure criterion of a laser weld shown in Equation (3) can be expressed as a function of the strain rate as follows: max. ϕ ( φ b( fn, fs, ε· ), φ i ( fn, fs, ε· ) ) = 1

(4a)

f n -⎞ 2 fn -⎞ ⎛ ----------fs -⎞ ⎛ ----------f 2 φ b ( fn, fs, ε· ) = ⎛⎝ -----------+ β ( ε· )⎛⎝ -----------+ ⎝ s -⎞⎠ ⎠ ⎠ ⎝ ⎠ · · · · F F FN ( ε ) FN ( ε ) S(ε) S(ε)

(4b)

fs φ i ( fn, fs, ε· ) = ----------------(4c) F*s ( fn, ε· ) where FN( ε· ) and FS( ε· ) are the strain-rate dependent

normal failure load and the strain-rate dependent virtual shear failure load of a laser weld in the base metal failure region, respectively. The variable β( ε· ) is a shape parameter that decides the shape in the failure contour of the base metal failure region. F*S( fn, ε· ) is the corresponding shear failure load for the normal load fn acting on the laser welds in the interfacial failure region. The strain-rate sensitivity of the shape parameter was investigated for the base metal failure criterion. The normalized failure contours of the 25 mm stitch-type laser welds of CR340 1.2t at various strain rates were constructed to examine the effect of the strain rate on the

Figure 11. The failure loadloading angle curves of laser-welded specimens at various loading angles and strain rates: (a) CR340 1.2t 25 mm stitch; (b) CR340 1.2t 20 mm stitch; (c) SPCC 1.0t 25 mm stitch; (d) CR340 φ 8 mm circle.

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Figure 12. Rate-dependent normal and shear failure load of the laser welds: (a) CR340 1.2t 25 mm stitch; (b) CR340 1.2t 20 mm stitch; (c) SPCC 1.0t 25 mm stitch; (d) CR340 φ 8 mm circle. shape of the failure contour. The normal and the shear failure loads at various strain rates were normalized. The normalized normal loads were calculated based on the failure load of a loading angle of 0o and the normalized shear failure loads were calculated based on the failure load of a loading angle of 75o. Figure 14 depicts the normalized failure contours of the 25 mm stitch-type laser welds of CR340 1.2t at various strain rates. The figure indicates that the failure contour takes similar shapes with various strain rates, which implies that the shape parameter β can be regarded as independent of the strain rate. The strain-rate sensitivity of the failure loads was investigated in the base metal failure region. The dynamic failure loads at various loading angles were normalized by the quasi-static loads. The normalized failure loads of the 25 mm stitch-type laser welds of CR340 1.2t were plotted in Figure 15 in the base metal failure region from 0o to 75o. On the average, the failure loads of 1 s-1, 10 s-1 and 100 s-1 increase by 7.9%, 13.6% and 16.3%, respectively, compared to the quasi-static failure load. The figure shows the strain rate effects on the normalized failure loads for a given loading angle, while those at a given strain rate are insensitive to the loading angles, which implies that the failure loads show similar strain-rate sensitivity regardless of the loading angles. Thus, the strain-rate sensitivities of the normal and the virtual shear failure loads are interpolated with the same functions as follows:

p ε·-⎞ ⎞ F( ε· ) = F0⎛⎝ 1 + C⎛⎝ ln --ε· 0⎠ ⎠

(5)

where F0 is the quasi-static failure load of the laser welds and ε· 0 is the reference strain rate at which the quasi-static tests are conducted. Figure 16 (a) shows the interpolation of the normal and the virtual shear failure load of the 25 mm stitch-type laser welds of CR340 1.2t using Equation (5) with respect to the logarithmic scale of the strain rate. The virtual shear failure loads at each strain rate were obtained after interpolating the experimental data with the base metal failure criterion of Equation (4b). The figures show that the exponential function of the logarithm of the strain rate provides an accurate description of the strain-rate sensitivity of the normal and the virtual shear failure loads obtained from dynamic failure tests. From Equations (4b) and (5) accompanying the strainrate independence of the failure parameter β, the dynamic failure criterion of the laser welds in the base metal failure region under combined normal and shear loading conditions can be expressed as follows: f n -⎞ 2 ⎛ -----------⎝ F ( ε· )⎠ + β N

fn -⎞ ⎛ ----------fn -⎞ ⎛ ----------fn -⎞ 2 ⎛ -----------⎝ F ( ε· )⎠ ⎝ F ( ε· )⎠ + ⎝ F ( ε· )⎠ = 1 N

S

p ε· -⎞ ⎞ FN ( ε· ) = FN0⎛⎝ 1 + C⎛⎝ ln ----ε· ref⎠ ⎠ p ε· -⎞ ⎞ FS ( ε· ) = FS0⎛ 1 + C⎛ ln ----⎝ ⎝ ε· ref⎠ ⎠

(6a)

S

(6b) (6c)

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 247

Figure 13. Strain-rate dependent failure contour of the laser welds at intermediate strain rates: (a) 25 mm stitch-type laser welds of CR340 1.2t; (b) 20 mm stitch-type laser welds of CR340 1.2t; (c) 25 mm stitch-type laser welds of SPCC 1.0t; (d) 8 mm diameter O-type laser welds of CR340 1.2t.

Figure 14. Normalized failure contours of the 25 mm stitch-type laser welds of CR340 1.2t at various strain rates in the base metal failure region. The coefficients of the proposed criterion of the laser welds for the base metal failure region have the following physical meanings: FN0 is the quasi-static normal failure load obtained directly from the experimental result, FS0 is the quasi-static virtual shear failure load obtained from the interpolation result of the experimental results, β is a shape

Figure 15. Normalized failure loads of the 25 mm stitchtype laser welds of CR340 1.2t at various loading angles in the base metal failure region.

parameter related to the shape of a failure contour, C and p are the coefficients of the strain-rate sensitivity, and ε· 0 is the reference strain rate at which the quasi-static failure test is conducted. The coefficients C and p can be obtained from regression analyses of the experimental data as shown in Figure 16 (a). The strain-rate sensitivity of the normal

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and the virtual shear failure loads for the 20 mm stitch-type laser welds of CR340 1.2t, the 25 mm stitch-type laser welds of SPCC 1.0t and the 8 mm diameter O-type laser welds of CR340 1.2t are plotted in Figure 17. The strainrate dependent failure contours of the 25 mm stitch-type laser welds of CR340 1.2t interpolated with the proposed dynamic failure criterion for the base metal failure region were compared to those obtained from the experiment as depicted in Figure 16 (b). Finally, the strain-rate effect on the failure loads was investigated in the interfacial failure region. In the interfacial failure region, the shear failure load decreases as the normal failure load decreases with an increase of the loading angle as shown in Figure 13. Therefore, the interfacial failure region is represented empirically in the form of a modified power law as shown in Equation (3d). The failure contour is extended with the increase of the strain rate. In order to consider the strain-rate effect on the pure-shear failure loads, the strain rate effect term on shear failure loads is multiplied by Equation (3d). The strain-rate sensitivity of the pure-shear failure loads is expressed as an exponential function based on the modified Johnson-Cook

Figure 17. The strain-rate sensitivity of the normal and the virtual shear failure loads for the various types of laser welds: (a) 20 mm stitch-type laser welds of CR340 1.2t; (b) 25 mm stitch-type laser welds of SPCC 1.0t; (c) 8 mm diameter O-type laser welds of CR340 1.2t.

Figure 16. Interpolation of the experimental data for the 25 mm stitch-type laser welds of CR340 1.2t using the proposed dynamic failure criterion of a laser weld in the base metal failure region: (a) normal and virtual shear failure loads; (b) strain-rate dependent failure contours.

model (Kang et al., 1999). In addition, the change in the shear failure load term with the increase of the strain rate is described by a function of the normal load and the strain rate based on the modified Khan-Huang-Liang model (Huh et al., 2012), which induces the increase or the decrease in the shear failure load of the normal load on the growth because of the change in the strain rate. Consequently, a new dynamic failure criterion of the laser welds for the interfacial failure region can be expressed as follows: n * m q ln ε· ε·-⎞ F*s ( fn, ε· ) = K a + ⎛⎝ 1 – ------------9⎞⎠ fn × 1 + D⎛⎝ ln --ln 10 ε· 0⎠

(7a)

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 249

fs ----------------=1 F*s ( fn, ε· )

(7b)

*

where, ε· = ε· ⁄ ε· 0 and ε· 0 is the reference strain rate at which quasi-static failure tests are conducted. F*s is the corresponding shear failure load for the normal load fn acting on the laser welds in the interfacial failure region. The constants in Equation (7a), K, a and n are the load coefficient, the additive normal load constant and the loadhardening exponent, respectively. The constants m, D and q are the coefficients of the strain-rate sensitivity. The coefficients D and q can be calculated from regression analyses of the experimental data shown in Figure 18 (a). The strain-rate sensitivity of the pure-shear failure load of the 20 mm stitch-type laser welds of CR340 1.2t, the 25 mm stitch-type laser welds of SPCC 1.0t and the 8 mm diameter O-type laser welds of CR340 1.2t are plotted in Figure 19. The strain-rate dependent failure contours of the 25 mm stitch-type laser welds of CR340 1.2t interpolated with the proposed dynamic failure criterion for the interfacial failure region were compared to those obtained from the experiment as depicted in Figure 18 (b). The constants of the proposed criterion for the interfacial failure region can be also obtained from this

Figure 19. The strain-rate sensitivity of the pure-shear failure load for various types of laser welds: (a) 20 mm stitch-type laser welds of CR340 1.2t; (b) 25 mm stitchtype laser welds of SPCC 1.0t; (c) 8 mm diameter O-type laser welds of CR340 1.2t. interpolation procedure. From Equations (6) and (7), a new dynamic failure criterion of laser welds under combined normal and shear loading conditions can be expressed as follows: max. ϕ ( φ b ( fn, fs, ε· ), φ i ( fn, fs, ε· ) ) = 1 Figure 18. Interpolation of the experimental data for the 25 mm stitch-type laser welds of CR340 1.2t using the proposed dynamic failure criterion of a laser weld in the interfacial failure region: (a) pure-shear failure load; (b) strain-rate dependent failure contours.

f n -⎞ 2 +β φ b ( fn, fs, ε· ) = ⎛⎝ -----------FN ( ε· )⎠

(8a)

fn -⎞ ⎛ ----------fs -⎞ ⎛ ----------fs -⎞ 2 ⎛ -----------⎝ F ( ε· )⎠ ⎝ F ( ε· )⎠ + ⎝ F ( ε· )⎠

p ε· -⎞ ⎞ FN ( ε· ) = FN0⎛⎝ 1 + C⎛⎝ ln ----ε· ref⎠ ⎠

N

S

(8b)

S

(8c)

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Table 9. Coefficients of the proposed dynamic failure criterion for the laser welds. Material and bead type

Base metal failure region FS0

Interfacial failure region

FN0 [kN]

[kN]

CR340 1.2t 25 mm stitch

12.06

16.17

0.41 0.0156 1.0798 12.83

0.1249 0.8991 0.0805 0.0156

1.0798

CR340 1.2t 20 mm stitch

9.21

11.68

0.59 0.0021 1.7276

9.61

0.0551 1.4906 0.0617 0.0051

1.4784

SPCC 1.0t 25 mm stitch

8.04

10.43

0.33 0.0021 1.5887

9.53

0.1733 0.6823 0.1184 0.0085

1.0304

CR340 1.2t φ 8 mm circle 10.15

16.02

1.39 0.0003 2.7045

8.92

1.8979 0.2646 0.1763 0.0003

2.7045

p ε· -⎞ ⎞ FS( ε· ) = FS0⎛ 1 + C⎛ ln ----⎝ ⎝ ε· ref⎠ ⎠

β

C

(8d)

fs φ i ( fn, fs, ε· ) = ------------------* Fs ( fn, ε· )

(8e)

· m n q lnε * ε·-⎞ F*s ( fn, ε· ) = K a + ⎛⎝ 1 – ------------9⎞⎠ fn × 1 + D⎛⎝ ln --ln 10 ε· 0⎠

(8f)

where Equation 8 (b) is the dynamic failure criterion for the base metal failure region, and Equation 8 (e) is the dynamic failure criterion for the interfacial failure region. The maximum value of the failure criteria is obtained after calculating the failure criteria of Equation 8 (b) and Equation 8 (d) with the normal load and the shear load acting on the laser welds under any strain rate. The failure mode and the onset of failure of the laser welds are determined when the maximum value reaches unity in Equation (8a). The coefficients of the 25 mm stitch-type laser welds of

p

K [kN]

α

m

n

D

q

CR340 1.2t and SPCC 1.0t, the 20 mm stitch-type laser welds of CR340 1.2t and the 8 mm diameter O-type laser welds of CR340 1.2t were determined using the experimental data shown in Table 9. The values of β obtained at a quasistatic state were used in the interpolation of the dynamic failure contours. The shape of the base metal failure criterion changes with the value of the shape parameter β. The safety region of the base metal failure criterion becomes smaller when the β value is closer to 2 and the base metal failure criterion takes the form of a straight line. On the other hand, the safety region of the base metal failure criterion becomes larger when the β value is closer to 0 and the shape of the base metal failure criterion takes the form of an ellipse when the value of β is zero. The β value of the stitch-type laser weld is closer to 0 than that of the O-type laser weld. Therefore, the stitch-type laser welds are safer than the O-type laser welds when the

Figure 20. Interpolation of the strain-rate dependent failure contour of the laser welds using the proposed dynamic failure criterion: (a) 25 mm stitch-type laser welds of CR340 1.2t; (b) 20 mm stitch-type laser welds of CR340 1.2t; (c) 25 mm stitch-type laser welds of SPCC 1.0t; (d) 8 mm diameter O-type laser welds of CR340 1.2t.

DYNAMIC FAILURE CHARACTERIZATION OF LASER WELDS UNDER COMBINED LOADING CONDITIONS 251

applied load to the stitch-type laser weld is coincident with the direction of the stitch-type laser weld. The strain-rate dependent failure contours of the 25 mm stitch-type laser welds of CR340 1.2t and SPCC 1.0t, the 20 mm stitch-type laser welds of CR340 1.2t and the 8 mm diameter O-type laser welds of CR340 1.2t interpolated with the proposed criterion were compared to those obtained from the experiment as depicted in Figure 20. The figures demonstrate that the proposed failure criterion provides a relatively good description of the failure contours for laser welds at intermediate strain rates.

4. CONCLUSION This paper proposes a new dynamic failure criterion of the laser weld under combined normal and shear loading conditions to predict the strain-rate dependent failure behavior of laser welds. The failure criterion had been developed based on the investigation of experimental results in nine different loading conditions considering the strain-rate effect on the failure loads. In order to evaluate the influence of the strain-rate on the failure loads with respect to the base metal and the bead geometry, the experiments were carried out with a high speed material testing machine at intermediate strain rates ranging from quasi-static to 100 s-1. The failure tests of both stitch-type and O-type laser welds of SPCC 1.0t and CR340 1.2t were carried out under the combined loading conditions with the variation of strain rate. The experimental results reveal that there exists a transition point around a loading angle of 75o due to the change of the failure mode from the base metal failure to the interfacial failure. The expansion of the failure loads were observed with the increase of the strain rate from 0.004 s-1 to 100 s-1. Based on the experimental data, a new dynamic failure criterion was developed for the description of the failure behavior of the laser welds based on the quasi-static failure criterion. The failure criteria are decomposed with two regions of the base metal failure and the interfacial failure. The proposed dynamic failure criterion can describe the expansion of the failure contours by considering the strain-rate effects on the failure load changes. The base metal failure region is expressed as a function of the normal and the virtual shear load, which is the so-called β-norm function, while the interfacial failure region is explained as a modified power law function. This proposed dynamic failure criterion of laser welds can be directly utilized for numerical simulation of crashworthiness assessment at the design stage of an auto-body to correctly predict the failure of laser welds and the subsequent deformation mode of an auto-body in the crash analysis.

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